DOI 10.4010/2016.947
ISSN 2321 3361 © 2016 IJESC
Research Article
Volume 6 Issue No. 4
Harmonics: What are they? What do they do?
Echegini Ngozi Silas1, Madubuike, Fidelia Ifeyinwa2
Mechatronic Instructor/Researcher at Skill ‘G’ Nigeria Limited, Abuja Nigeria1
Electronics Engineering Instructor/Researcher at Skill 'G' Nigeria Limited, Abuja Nigeria2
silasngoziechegini@gmail.com1, delia4nneoma@gmail.com2
Abstract:
Harmonics are everywhere just as the air is everywhere. As long as there is some form of wave signal characterized by a certain
frequency, there is bound to be a harmonic signal. The phenomenon is a vital one with respect to electronics, electromagnetism,
electric fields and various forms of wave. A harmonic is a signal or wave whose frequency is a whole number multiple of the
frequency of some reference signal or wave. For instance, if the frequency of a reference signal is ‘f’, then the harmonics will be in
the order (f, 2f, 3f, …. And so on). Thus, the first harmonic is usually the same as the frequency of the reference signal and we have
the second, third, etc. harmonic. Signals occurring at frequencies of 2 f , 4 f , 6 f , etc. are called even harmonics; the signals at
frequencies of 3 f , 5 f , 7 f , etc. are called odd harmonics. A signal can, in theory, have infinitely many harmonics. The term can
also refer to the ratio of the frequency of such a signal or wave to the frequency of the reference signal or wave. If ‘f’ represent the
fundamental frequency of an AC signal, electromagnetic field or sound wave, this frequency, usually expressed in hertz is the
frequency at which most of the energy is contained, or at which the signal is defined to occur. If the signal is displayed on an
oscilloscope, the waveform will appear to repeat at a rate corresponding to f Hz.
1.
INTRODUCTION:
Most signals contain energy at harmonic frequencies in
addition to the energy at the fundamental frequency. A
signal will be a perfect sine wave if all the energy in that
signal is contained at the fundamental frequency. On the
contrary, the event where the signal is not a perfect sine
wave implies that some energy is contained in the
harmonics. Some waveforms contain large amounts of
energy at harmonic frequencies. Typical are square waves,
saw-tooth waves, and triangular waves.
2.
What are harmonics?
Harmonics allow for the representation of any periodic
waveform. In fact, according to Fourier’s theorem, any
periodic function of a period T may be represented as a
summation of:

A sinusoid with the same period T;

Some sinusoids with the same frequency as whole
multiples of the fundamental;

A possible continuous component, if the function
has an average value not null in the period.
Thus, we can say that harmonics are nothing less than the
components of a distorted waveform and their use allows us
to analyze any periodic nonsinusoidal waveform through
different sinusoidal waveform components.
International Journal of Engineering Science and Computing, April 2016
The equation for the harmonic expansion of a periodic
function is presented below:
Where:
– Value of the DC component, generally zero and
considered as such hereinafter,
– rms value of the nth harmonic,
ω – angular frequency of the fundamental frequency,
– displacement of the harmonic component at t = 0.
Any harmonic with frequency corresponding to the period of
the original waveform is called fundamental and the
harmonic with frequency equal to “n” times that of the
fundamental is called harmonic component of order “n”.
A perfectly sinusoidal waveform complying with Fourier’s
theorem does not present harmonic components of order
different from the fundamental one.
Therefore, it is understandable how there are no harmonics
in an electrical system when the waveforms of current and
voltage are sinusoidal. On the contrary, the presence of
harmonics in an electrical system is an index of the
distortion of the voltage or current waveform and this
implies such a distribution of the electric power that
malfunctioning of equipment and protective devices can be
caused.
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This nonsinusoidal waveform can be deconstructed into
harmonics. If the network impedances are very low, the
voltage distortion resulting from a harmonic current is low
too and rarely above the pollution level already present in
the network. As a consequence, the voltage can remain
practically sinusoidal also in the presence of current
harmonics.
To function properly, many electronic devices need a
definite current waveform and thus they have to ’cut’ the
sinusoidal waveform so as to change its rms value or to get a
direct current from an alternate value. In these cases the
current on the line has a nonsinusoidal curve.
Figure (1) is a graphical representation of this concept.
3. How harmonics are generated:
Harmonics are generated by non-linear loads. A load is said
to be non-linear when the current it draws does not have the
same wave form as the supply voltage. Devices comprising
power electronics circuits are typical non-linear loads. Such
loads are increasingly frequent and their percentage in
overall electrical consumption is growing steadily. When we
apply a sinusoidal voltage to a load of this type, we shall
obtain a current with non-sinusoidal waveform. The diagram
of Figure (2) illustrates an example of nonsinusoidal current
waveform due to a nonlinear load:
Figure 2 – Left: Linear load waveform; Right: Non-linear
load waveform
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3.1 Equipment generating harmonics include:
 Personal computer
 Fluorescent lamps
 Static converters
 Continuity groups
 Variable speed drives
 Welders
In general, waveform distortion is due to the presence of
bridge rectifiers (inside of these equipment), whose
semiconductor devices carry the current only for a fraction
of the whole period, thus originating discontinuous curves
with the consequent introduction of numerous harmonics.
Also transformers can be a cause of harmonic pollution. In
fact, by applying a perfectly sinusoidal voltage to a
transformer, it results into a sinusoidal magnetizing flux.
However, due to the phenomenon of the magnetic saturation
of iron, the magnetizing current shall not be sinusoidal.
Figure 3 shows a graphic representation of this
phenomenon: Phenomenon of the magnetic saturation of
transformer iron
The resultant waveform of the magnetizing current contains
numerous harmonics, the greatest of which is the third one.
However, it should be noted that the magnetizing current is
generally a little percentage of the rated current of the
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transformer and the distortion effect becomes more and more
negligible the most loaded the transformer results to be.
3.1.1 The main problems caused by harmonic currents
are:
i. overloading of neutrals
ii. Increase of losses in the transformers
iii. Increase of skin effect
3.1.2 The main effects of the harmonics voltages are:
iv. voltage distortion
v. disturbances in the torque of induction motors
i.
Overloading of neutrals:
In a three phase symmetric and balanced system with
neutral, the waveforms between the phases are shifted by a
120° phase angle so that, when the phases are equally
loaded, the current in the neutral is zero.
The presence of unbalanced loads (phase-to-phase, phase-toneutral etc.) allows the flowing of an unbalanced current in
the neutral
The same is true also for the harmonics multiple of three
(even and odd, although actually the odd ones are more
common).
ii.
Increase of losses in the transformers
The effects of harmonics inside the transformers involve
mainly three aspects:
a. Increase of iron losses (or no-load losses)
b. Increase of copper losses
c. Presence of harmonics circulating in the windings
The iron losses are due to the hysteresis phenomenon and to
the losses caused by eddy currents. The losses due to
hysteresis are proportional to the frequency, whereas the
losses due to eddy currents depend on the square of the
frequency.
Figure (4) – Unbalanced system of currents
Figure 4 above shows an unbalanced system of currents
(phase 3 with a load 30% higher than the other two phases),
and the current resultant in the neutral is highlighted in red.
Under these circumstances, the Standards allow the neutral
conductor to be dimensioned with a cross section smaller
than the phase conductors.
Although the currents at fundamental frequency in the three
phases cancel each other out, the components of the third
harmonic, having a period equal to a third of the
fundamental, that is equal to the phase shift between the
phases (see Figure 5 below), are reciprocally in phase and
consequently they sum in the neutral conductor adding
themselves to the normal unbalance currents.
International Journal of Engineering Science and Computing, April 2016
Figure 5 – Fundamental harmonic and 3rd harmonic
The copper losses correspond to the power dissipated by
Joule effect in the transformer windings. As the frequency
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rises (starting from 350 Hz) the current tends to thicken on
the surface of the conductors (skin effect). Under these
circumstances, the conductors offer a smaller cross section to
the current flow, since the losses by Joule effect increase.
These two first aspects affect the overheating which
sometimes causes a derating of the transformer.
Harmonic distortion is present to some degree on all power
systems.
Fundamentally, one needs to control harmonics only when
they become a problem. Harmonic distortion is not a new
phenomenon on power systems.
The third aspect is relevant to the effects of the triple-N
harmonics (homopolar harmonics) on the transformer
windings. In case of delta windings, the harmonics flow
through the windings and do not propagate upstream towards
the network since they are all in phase.
The delta windings therefore represent a barrier for triple-N
harmonics, but it is necessary to pay particular attention to
this type of harmonic components for a correct
dimensioning of the transformer.
iii.
Increase of skin effect
When the frequency rises, the current tends to flow on the
outer surface of a conductor. This phenomenon is known as
skin effect and is more pronounced at high frequencies.
At 50 Hz power supply frequency, skin effect is
negligible, but above 350 Hz, which corresponds to the 7th
harmonic, the cross section for the current flow reduces, thus
increasing the resistance and causing additional losses and
heating.
In the presence of high-order harmonics, it is necessary to
take skin effect into account, because it affects the life of
cables. In order to overcome this problem, it is possible to
use multiple conductor cables or bus-bar systems formed
by more elementary isolated conductors.
iv.
Voltage distortion
The distorted load current drawn by the nonlinear load
causes a distorted voltage drop in the cable impedance. The
resultant distorted voltage waveform is applied to all other
loads connected to the same circuit, causing
harmonic currents to flow in them, even if they are linear
loads.
The solution consists in separating the circuits which supply
harmonic generating loads from those supplying loads
sensitive to harmonics.
v. Disturbances in the torque of induction motors
Harmonic voltage distortion causes increased eddy current
losses in the motors, in the same way as seen for
transformers. The additional losses are due to the generation
of harmonic fields in the stator, each of which is trying to
rotate the motor at a different speed, both forwards (1st, 4th,
7th, …) as well as backwards (2nd, 5th, 8th, …).
High frequency currents induced in the rotor further increase
losses.
4. Principles of controlling harmonics
i.
Harmonic distortion is caused by nonlinear
devices in the power system. A nonlinear device is one in
which the current is not proportional to the applied voltage.
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Figure (6) - Variation of the voltage THD over a 1-week
period
4.1 There are three common causes of harmonic
problems:
a. The source of harmonic currents is too great.
b.
The path in which the currents flow is too long
(electrically), resulting in either high voltage distortion or
telephone interference.
c. The response of the system magnifies one or more
harmonics to a greater degree than can be tolerated.
When a problem occurs, the basic options for controlling
harmonics are:
a. Reduce the harmonic currents produced by the load.
b. Add filters to siphon the harmonic currents off the
system, block the currents from entering the system, or
supply the harmonic currents locally.
c. Modify the frequency response of the system by filters,
inductors, or capacitors.
Reducing harmonic currents in loads
There is often little that can be done with existing load
equipment to significantly reduce the amount of harmonic
current it is producing unless it is being mishandled. While
an overexcited transformer can be brought back into normal
operation by lowering the applied voltage to the correct
range, arcing devices and most electronic power converters
are locked into their designed characteristics.
Pulse Width Modulator drives that charge the dc bus
capacitor directly from the line without any intentional
impedance are one exception to this. Adding a line reactor or
transformer in series will significantly reduce harmonics, as
well as provide transient protection benefits.
Transformer connections can be employed to reduce
harmonic currents in three-phase systems. Phase-shifting
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half of the 6-pulse power converters in a plant load by 30°
can approximate the benefits of 12- pulse loads by
dramatically reducing the fifth and seventh harmonics.
Delta-connected transformers can block the flow of zerosequence harmonics (typically triplens) from the line. Zigzag
and grounding transformers can shunt the triplens off the
line.
Purchasing specifications can go a long way toward
preventing harmonic problems by penalizing bids from
vendors with high harmonic content. This is particularly
important for such loads as high-efficiency lighting.
ii.
Filtering
The shunt filter works by short-circuiting harmonic currents
as close to the source of distortion as practical. This keeps
the currents out of the supply system. This is the most
common type of filtering applied because of economics and
because it also tends to correct the load power factor as well
as remove the harmonic current.
e.
Remove the capacitor and simply accept the higher
losses, lower voltage, and power factor penalty. If
technically feasible, this is occasionally the best economic
choice.
5. And now, how do we get rid of Harmonics?
A load that is purely resistive has the same wave shapes for
voltage and current. Both are normally pure sinusoids. Most
induction motors fed directly from AC mains also behave in
a similar manner except that they draw some reactive load as
well. The current waveform is still sinusoidal (see Figure 7).
However, the current waveform gets distorted when power
electronic devices are introduced in the system to control the
speed of motors.
These devices chop off part of the AC waveform using
thyristors or power transistors, which are used as static
switches.
Another approach is to apply a series filter that blocks the
harmonic currents. This is a parallel-tuned circuit that offers
a high impedance to the harmonic current. It is not often
used because it is difficult to insulate and the load voltage is
much distorted. One common application is in the neutral of
a grounded-wye capacitor to block the flow of triple
harmonics while still retaining a good ground at fundamental
frequency.
Active filters work by electronically supplying the harmonic
component of the current into a nonlinear load.
Modifying the system frequency response
4.2 There are a number of methods to modify adverse
system responses to harmonics:
a. Add a shunt filter. Not only does this shunt a
troublesome harmonic current off the system, but it
completely changes the system response, most often, but not
always, for the better.
b. Add a reactor to detune the system. Harmful resonances
generally occur between the system inductance and shunt
power factor correction capacitors. The reactor must be
added between the capacitor and the supply system source.
One method is to simply put a reactor in series with the
capacitor to move the system resonance without actually
tuning the capacitor to create a filter. Another is to add
reactance in the line.
c. Change the capacitor size. This is often one of the least
expensive options for both utilities and industrial customers.
d. Move a capacitor to a point on the system with a
different short-circuit impedance or higher losses. This is
also an option for utilities when a new bank causes telephone
interference—moving the bank to another branch of the
feeder may very well resolve the problem. This is frequently
not an option for industrial users because the capacitor
cannot be moved far enough to make a difference.
International Journal of Engineering Science and Computing, April 2016
Figure (7) – Voltage and current waveforms of an induction
motor
Such altered waveforms may be mathematically analyzed
using Fourier transforms as a combination of vectors of the
power frequency (50/60 Hz) and others whose frequency is
a multiple of the power frequency.
The power frequency component is called the
fundamental and higher multiples are called harmonics. It
should be remembered that all electrical generators produce
only voltage at fundamental frequency.
But there has to be a source if a harmonic current has to
flow. It is therefore construed theoretically that all harmonicproducing loads are current sources of harmonics. These
sources drive harmonic currents through the rest of
the system consisting of the source as well as other loads
connected to it.
These currents flowing through the different impedances of
the system appear as harmonic voltages. It is usual for
the voltage waveform of such a system to appear distorted.
Also, the harmonic currents flowing through the other loads
of the system give rise to several abnormalities (refer Table
1 below).
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Table 1 – Effects harmonics have on different system
components
EQUIPMENT
EFFECTS OF HARMONICS
Amplify harmonics on electrical
Capacitors
distribution system.
Phase
and
neutral
conductors
Electrical wiring
undersized.
Transferring capability and operation
Engine generators
disrupted.
May fail prematurely due to fifth
Induction motors
harmonic
Metering
Inaccurate measurement of power
Over
current
Breaker and fuse nuisance tripping
protection
Sensitive electronic
Voltage drop between neutral and earth
loads
Transformers
Decreased efficiency and overheating
Uninterruptible
Line and load interaction
power systems
An example how shunt filters function:
Let us see how these shunt filters function. We can use a
computer to show what happens as harmonics are filtered
from a distorted wave.
The example chosen is a 120° square wave current with a
10°commutation time; a typical line current waveform for
a DC motor drive and for many AC drives. Here is the
square wave before any filtering. The distortion factor
is 26% not too pretty a waveform (Figure 8a). Now let us
take out the fifth harmonic.
This may not look a whole lot better, but the distortion factor
is down from 26 to 18%, so things are improving (Figure
8b).
Now let us take out the seventh as well. Things are actually
looking better now. We can see the sine wave starting to
emerge. Distortion factor is down to 11% (Figure 8c).
Next, we take out the eleventh. Still no beauty queen, but
the distortion factor is now only 8% (Figure 8d).
Let us add in the final element and remove the
thirteenth harmonic. This
is
our
final
current
waveform (Figure 8e). The distortion factor is 6%, so we
are putting a reasonable current into the utility. Of course,
the significance of this current waveform to the voltage
distortion would depend on the source impedance and
the current level.
Higher-frequency harmonics can be propagated by the power
conductors acting as antennae and appear as induced noise
voltages in nearby signal circuits.
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Figure (8) – Reduction of harmonics by filters
6. SUMMARY
It is not possible to prevent harmonic currents altogether.
But they can be prevented from flowing through the entire
system by providing a separate low-impedance path for
them. This is done by the use of adequately rated series
tuned circuits consisting of a reactor and capacitor, which
have equal impedance at a specific harmonic frequency.
Several such tuned banks (one for each harmonic frequency)
will be needed to totally divert all harmonics away from
the system. However, for practical reasons, only a few of the
lower order harmonics with larger magnitudes are filtered
out, which is adequate to provide substantial reduction of
harmonic content.
Figure 2 shows how a filter might remove the highfrequency components and how the wave shape might
appear as the removal takes place.
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